Question

The question says express each repeating decimal as a fraction:

5.23232323

This is my work but my answer doesn't seem right:

100x= 523.23232323
- 10x= 52.23232323
90x= 470.909090
/ 90x. \90x
x= 5.23232323

What am I doing wrong?
And how am I suppose to know when to multiply x by 10,100, or 1000?
Thank you!!

Answer 1

I'd read the decimal as a fraction.

5.23 = 5 2323/10000 = 5 23/100

Answer 2

just use your decimal
let x = .232323...
100x = 23.232323...
subtract them:
99x = 23
x = 23/99

so 5.2323.... = 5 23/99 or 518/99

check with your calculator to verify it to be correct.